I've had similar problems with Mint on a couple of machines. I agree with you that it's probably just your graphics driver.
If your motherboard has built-in graphics you could try removing your NVIDIA card and connecting your monitor to the motherboard. If the graphics work in this setup you could then go ahead and download all of the updates for your version of Linux. Then reinstall your graphics card and reboot to see if the Linux generic NVIDIA driver will run.
I've done this a few times with success.
I've running older NVIDIA cards on my two Linux Mint machines. Mint 17.3 32-Bit runs the proprietary NVIDIA driver just fine.
My other machine is running 18.2 KDE 64-Bit. The NVIDA driver for this machine gave me a lot of quirky problems. This machine actually runs better using the generic Linux Nouveau driver.
In one of these machines (can't remember which) I actually had to go into the BIOS and flick a switch off to get the graphics to behave.
Sounds like you know the source of the problem.
Good luck!
I just looked at the specs for your computer. No motherboard graphics.
If you have an older graphics card you might try slipping that in temporarily to see if you can finish updating the Mint OS.